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A solid mixture contains \(\mathrm{MgCl}_{2}\) and NaCl. When \(0.5000 \mathrm{~g}\) of this solid is dissolved in enough water to form \(1.000 \mathrm{~L}\) of solution, the osmotic pressure at \(25.0^{\circ} \mathrm{C}\) is observed to be \(0.3950\) atm. What is the mass percent of \(\mathrm{MgCl}_{2}\) in the solid? (Assume ideal behavior for the solution.)

Short Answer

Expert verified
The mass percent of MgCl鈧 in the solid mixture is approximately \(38.68\%\).

Step by step solution

01

Write down the formula for osmotic pressure.

We will be using the osmotic pressure formula to relate the moles of solute particles to the osmotic pressure: Osmotic pressure (蟺) = (n/V) 脳 R 脳 T where: n = moles of solute particles V = volume of the solution R = ideal gas constant (0.0821 L路atm/mol路K) T = temperature (in Kelvin)
02

Express the moles of solute particles in terms of concentration of MgCl鈧 and NaCl.

Let x be the mass of MgCl鈧 in the 0.5000 g mixture. Then, the mass of NaCl is (0.5000 - x) g. We can express the moles of solute particles (n) in terms of concentration (C) of MgCl鈧 and NaCl as follows: n = (x / M鈧) 脳 2 + ((0.5000 - x) / M鈧) where: M鈧 = molar mass of MgCl鈧 (95.211 g/mol) M鈧 = molar mass of NaCl (58.443 g/mol) 2 is a factor considering that MgCl鈧 and NaCl dissociate into 2 and 1 particles in the solution, respectively.
03

Convert the temperature to Kelvin and substitute values into the osmotic pressure formula.

To convert the given temperature from Celsius to Kelvin, we add 273.15: T = 25.0掳C + 273.15 = 298.15 K Now, substitute the values into the osmotic pressure formula: 0.3950 atm = [(x / 95.211) 脳 2 + (0.5000 - x) / 58.443] 脳 (0.0821 L路atm/mol路K) 脳 298.15 K / 1.000 L
04

Solve for x.

To solve for x, we can now rearrange the equation and solve for x using algebra: x = (0.3950 atm 脳 1.000 L) / [(0.0821 L路atm/mol路K) 脳 298.15 K] - (0.5000 - x) / 58.443 脳 95.211 / 2 Solve for x: x 鈮 0.1934 g
05

Calculate the mass percent of MgCl鈧.

Now, we can calculate the mass percent of MgCl鈧 in the solid mixture as follows: Mass percent of MgCl鈧 = (Mass of MgCl鈧 / Total mass) 脳 100% Mass percent of MgCl鈧 = (0.1934 g / 0.5000 g) 脳 100% Mass percent of MgCl鈧 鈮 38.68% The mass percent of MgCl鈧 in the solid mixture is approximately 38.68%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

ideal gas constant
When calculating osmotic pressure, you'll often encounter the ideal gas constant, denoted by "R." This constant is central to many equations in chemistry and physics, serving as a bridge between different properties of gases. In the context of osmotic pressure, it helps relate the temperature and volume of a solution to the pressure exerted by solute particles.
The value of the ideal gas constant is typically given as 0.0821 L路atm/mol路K. It is a unit-specific constant, meaning it must match the units of the other variables it interacts with, such as pressure (atm), volume (L), moles (mol), and temperature (Kelvin).
In calculations, this constant lets us understand how temperature changes or the amount of solute in a solution can affect the pressure. For example, you multiply "R" by both temperature and the number of moles to contribute to osmotic pressure, enabling precise predictions of behavior in solutions at varying conditions.
molar mass
The term "molar mass" refers to the mass of one mole of a substance, expressed in grams per mole (g/mol). It's a critical concept when dealing with chemical calculations because it lets you convert between the mass of a substance and the amount in moles.
For the compounds mentioned in the exercise, the molar mass of MgCl鈧 is 95.211 g/mol, and for NaCl, it is 58.443 g/mol. Knowing these values is essential for converting from grams to moles, which is crucial in determining the number of particles in a solution, especially in osmotic pressure calculations.
Molar mass acts as a conversion factor. If you know the mass of a substance, you can easily find out how many moles you have, thus allowing for stoichiometric calculations and predictions of how a solution will behave under different conditions.
mass percent
Mass percent is a simple yet vital concept used to describe the concentration of a particular component in a mixture. It's expressed as the mass of the component divided by the total mass of the mixture, multiplied by 100% to convert it into a percentage.
For instance, in the scenario described, we calculated the mass percent of MgCl鈧 in the solid mixture. This involved dividing the mass of MgCl鈧 found through calculations (0.1934 g) by the total mixture mass (0.5000 g), then multiplying by 100% to get approximately 38.68%.
Using mass percent is helpful for several reasons:
  • It is dimensionless and easy to understand.
  • It allows direct comparison between different solutions or mixtures.
  • It's a straightforward way to convey how much of a component is present relative to the whole.
Mass percent can reveal composition and purity and is crucial in preparing solutions with precise concentrations.
dissociation in solutions
Dissociation in solutions is a process where compounds split into smaller particles, typically ions, when dissolved in a solvent. This is a particularly important concept in chemical reactions and solutions' behavior.
For instance, in our problem, MgCl鈧 dissociates into three ions (one Mg虏鈦 and two Cl鈦 ions), while NaCl dissociates into two ions (one Na鈦 and one Cl鈦 ion) in the solution. This dissociation directly impacts osmotic pressure because the presence of more particles in solution increases the pressure exerted by the solute.
Important points about dissociation:
  • The extent of dissociation affects the number of particles in the solution.
  • Increased number of particles leads to higher osmotic pressure.
  • Complete and partial dissociation can alter the solution's electrical conductivity and physical properties.
Dissociation is essential for predicting how solutions will conduct electricity, their reaction kinetics, and properties like osmotic pressure, all of which are significant in both lab and real-world applications.

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Most popular questions from this chapter

Erythrocytes are red blood cells containing hemoglobin. In a saline solution they shrivel when the salt concentration is high and swell when the salt concentration is low. In a \(25^{\circ} \mathrm{C}\) aqueous solution of \(\mathrm{NaCl}\), whose freezing point is \(-0.406^{\circ} \mathrm{C}\), erythrocytes neither swell nor shrink. If we want to calculate the osmotic pressure of the solution inside the erythrocytes under these conditions, what do we need to assume? Why? Estimate how good (or poor) of an assumption this is. Make this assumption and calculate the osmotic pressure of the solution inside the erythrocytes.

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